Short Notes on Theory of Signal Detection Walter Schneider

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Short Notes on Theory of Signal DetectionWalter
Schneider

• Links
• calculator http//wise.cgu.edu/sdtmod/index.asp
• handout http//www.cns.nyu.edu/david/handouts/sd
  t/sdt.html

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Normal Distribution
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Hit/Miss Criterion
  Turor No Tumor
Say Tumor Hit False Alarm
Say No Turmor" Miss Correct Rejection
  Turor No Tumor
Say Tumor 40 5
Say No Turmor" 10 45
TOTAL 50 50
The hit rate is 40/50 or as a proportion .80. The
false alarm rate is 5/50 or .10.
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Criterion Shift
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d and ROC
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Basic Curves
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d - Sensitivity

• The formula for d' is
• d z(p(False Alarms))- z(p(Hits))
• where z (H) and z (FA) represent the
  transformation of the hit and false alarm rates
  to z-scores.
• Example
• False Alarms 0.10, Hits 0.70,
• d Z (0.10) Z (0.70) 1.28 -0.52 1.8

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Beta - Criterion

• Criterion bias ordinate of hit/ ordinate FA
• The formula for d' is
• Beta Ordinate p(Hit) / Ordinate
  p(FalseAlarm)
• Example False Alarms 0.10, Hits 0.70,
• Beta Ordinate (0.70) / Ordinate (0.10)
• 0.349 / 0.176 1.98

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Example of Mean 3 subjects
d z(p(False Alarms))- z(p(Hits))
Beta Ordinate p(Hit) / Ordinate
p(FalseAlarm)
Note d and Beta must be calculated for each run
of an expected sensitivity and criterion
separately
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Practical Considerations

• Need significant FAs and misses (gt10)
• (NOTE A less sensitive to low FAs)
• Data must be done with consistent bias and
  sensitivity
• Calculations must be done within subject and if
  need be within run
• To determine average d and beta calculate the
  individual estimates (DO NOT AVERAGE THE RAW HITS
  AND FALSE ALARMS)